arXiv:2603. 08825v2 Announce Type: replace-cross Abstract: Discrete graph generation has emerged as a powerful paradigm for modeling graph-structured data, yet state of the art models often rely on Graph Transformers or higher order architectures.
arXiv:2607. 15773v1 Announce Type: new Abstract: Higher-order couplings enhance the expressive power of hypergraph neural networks (HGNNs), but they also intensify representation collapse in deep propagation due to strong multi-way feature mixing.
The paper studies the stability of graph-aware continuous‑time generative models that use a graph filter combined with a learned graph neural network. It derives explicit Wasserstein bounds showing how relative graph perturbations affect the generated distributions, and proposes a principled framework for designing stable graph filters that preserve heat‑diffusion smoothing while improving structural stability. Experiments on synthetic and fMRI data demonstrate that these stable filters enhance robustness and match or surpass the generative quality of a heat‑equation baseline.
arXiv:2607. 28185v1 Announce Type: new Abstract: Oversmoothing is a fundamental limitation of deep graph neural networks (GNNs), where repeated message passing causes node representations to become increasingly similar, eventually collapsing toward a low-dimensional subspace.
arXiv:2608. 07161v1 Announce Type: cross Abstract: Simulating complex fluid flows requires capturing full equilibrium distributions rather than just mean trajectories, yet high-fidelity solvers remain computationally prohibitive.
The paper explores how information propagates in Deep Graph Networks (DGNs) for both static and dynamic graphs, treating DGNs as dynamical systems. It presents new architectures that better preserve long‑term node dependencies and learn complex spatio‑temporal patterns from irregular, sparsely sampled dynamic graphs. The work combines theoretical analysis with empirical results to demonstrate the effectiveness of these designs.
arXiv:2607. 07510v1 Announce Type: cross Abstract: Generating signals on graphs requires permutation-equivariant models that exhibit stability with respect to relative structural perturbations.
Generating signals on graphs requires permutation-equivariant models that exhibit stability with respect to relative structural perturbations. While favorable stability properties of Graph Neural Networks (GNNs) have been well documented, it is unclear how structural errors propagate through the dynamics of continuous generative flow models that are gaining traction for graph signal generation.
The paper investigates how the choice of graph tokenization affects transformer expressivity. It analyzes three tokenization families—spectral, random‑walk, and adjacency—showing that each induces different depth requirements and that some tokenizations are inherently lossy or ill‑conditioned for certain tasks. The authors prove lower bounds and impossibility results for converting between tokenizations and validate these findings with experiments on synthetic and real‑world data.
Oversmoothing is a fundamental limitation of deep graph neural networks (GNNs), where repeated message passing causes node representations to become increasingly similar, eventually collapsing toward a low-dimensional subspace. This phenomenon limits the effective depth of message-passing architectures and motivates the search for mechanisms that preserve representation diversity.
The paper introduces RGC‑Net, a Reservoir‑Based Graph Convolutional Network that combines fixed‑random reservoir dynamics with a structured convolutional framework for graph learning. It addresses limitations of existing reservoir‑based GNNs by adding a leaky integrator for better feature retention and a robust, adaptable architecture for graph classification and generation. Experiments demonstrate state‑of‑the‑art performance on classification and generative tasks, including dynamic brain connectivity, with faster convergence and reduced over‑smoothing.
HyPE-GT introduces a framework that generates learnable hyperbolic positional encodings for Graph Transformers, enabling the capture of complex hierarchical relationships in graph-structured data. Unlike traditional Euclidean encodings, HyPE’s hyperbolic encodings can be selected to suit specific downstream tasks and help mitigate oversmoothing in deep Graph Neural Networks. Experiments on molecular benchmarks and large-scale Open Graph Benchmark datasets demonstrate improved performance, while additional tests on Coauthor and Copurchase networks confirm HyPE’s effectiveness in controlling oversmoothing.